VII. Seki's contemporaries and possible Western influences. 133
was a Japanese student of mathematics in Holland during Seki's time,1 doubtless escaping by means of one of the Dutch trading vessels from Nagasaki. We know nothing of his Japanese name, but the Latin form adopted by him was Petrus Hartsingius, and we know that he studied under Van Schooten at Leyden. That he was a scholar of some distinction is seen in the fact that Van Schooten makes mention of him in his Tractatus de concinnandis demonstrationibus geometricis ex calculo algebraico in one of his editions of Descartes's La Gcomctrie^ as follows: "placuit majoris certitudinis ergo idem Theorema Synthetic^ verificare, procendo sa concessis ad quaesita, prout ad hoc me instigavit praestantessimus ac undequaque doctissimus juvenis D. Petrus Hartsingius, lapo-nensis, quondam in addiscendis Mathematis, discipulus meus solertissimus."3 The passage in Van Schooten was first noticed by Giovanni Vacca, who communicated it to Professor Moritz Cantor.
Some further light upon the matter is thrown by a record in the Alburn Studios ormn Academiae Lugduno Batavaep as follows:
"Petrus Hartsingius Japonensis, 31, M. Hon. C." with the date May 6, 1669. Here the numeral stands for the age of the student, M. for medicine, his major subject, and Hon. C. for Honoris Causa, his record having been an honorable one.
1 HARZER, P., Die exaden Wissenschaften im alien Japan, Jahresbericht der deutschen Mathematiker-Vereinigitng, Bd. 14, 1905, Heft 6; MIKAMI, Y., Z/er Frage abendlandischer Einfliisse auf die japanische Mathematik am Ende ties siebzehnten Jahrhundefts, Blbliotkeca Mathematlca, Bd. VII (3), Heft 4.
2 HARZER quotes from the 1661 edition, p. 413. We have quoted from the Amsterdam edition of 1683, p. 413.
3 T. HAYASHI remarks that the same words appear in a posthumous work of Van Schooten's, but this probably refers to the above editio tertia of 1683. See HAYASHI, T., On the Japanese who was in Europe about ike middle of the seventeenth century (in Japanese), Journal of the Tokyo Physics School, Mav, 1905; MiKAMf, Y., Hatono Soha and the mathematics of Seki, in the Nieuiv ArchieJ voor Wiskunde, tweede Reeks, Negende Deel, 1910.
4 Hague, 1875. It gives a list of students and professors from 1575 to 1875.